X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/ThesisAli.git/blobdiff_plain/00e1a4c411c07d09489772c40f87682af1425f48..b526efd6a44846d1d89a70fedae4bf9bd2058885:/CHAPITRE_05.tex

diff --git a/CHAPITRE_05.tex b/CHAPITRE_05.tex
index 714ecd7..2ee5579 100644
--- a/CHAPITRE_05.tex
+++ b/CHAPITRE_05.tex
@@ -11,28 +11,10 @@
 \section{Introduction}
 \label{ch5:sec:01}
 
-\indent  The fast  developments of low-cost  sensor devices  and  wireless
-communications have allowed the emergence of WSNs. A WSN includes a large number
-of small, limited-power sensors that  can sense, process, and transmit data over
-a wireless  communication. They communicate  with each other by using multi-hop
-wireless communications and cooperate together  to monitor the area of interest,
-so that  each measured data can be  reported to a monitoring  center called sink
-for further  analysis~\cite{ref222}.  There  are several fields  of application
-covering  a wide  spectrum for a  WSN, including health, home, environmental,
-military, and industrial applications~\cite{ref19}.
-
-On the one hand sensor nodes run on batteries with limited capacities, and it is
-often  costly  or  simply  impossible  to  replace  and/or  recharge  batteries,
-especially in remote and hostile environments. Obviously, to achieve a long life
-of the  network it is important  to conserve battery  power. Therefore, lifetime
-optimization is one of the most critical issues in wireless sensor networks. On
-the other hand we must guarantee  coverage over the area of interest. To fulfill
-these two objectives, the main idea  is to take advantage of overlapping sensing
-regions to turn-off redundant sensor nodes  and thus save energy. In this paper,
-we concentrate  on the area coverage  problem, with the  objective of maximizing
-the network lifetime by using an optimized multiround scheduling.
-
-We study the problem of designing an energy-efficient optimization algorithm that divides the sensor nodes in a WSN into multiple cover sets such that the area of interest is monitored as long as possible. Providing multiple cover sets can be used to improve the energy efficiency of WSNs. Therefore, in order to increase the longevity of the WSN and conserve the energy, it can be useful to provide multiple cover sets in one time after that schedule them for multiple rounds, so that the battery life of a sensor is not wasted due to the repeated execution of the coverage optimization algorithm, as well as the information exchange and leader election.
+%The fast  developments of low-cost  sensor devices  and  wireless communications have allowed the emergence of WSNs. A WSN includes a large number of small, limited-power sensors that  can sense, process, and transmit data over a wireless  communication. They communicate  with each other by using multi-hop wireless communications and cooperate together  to monitor the area of interest, so that  each measured data can be  reported to a monitoring  center called sink for further  analysis~\cite{ref222}.  There  are several fields  of application covering  a wide  spectrum for a  WSN, including health, home, environmental, military, and industrial applications~\cite{ref19}.
+
+%On the one hand sensor nodes run on batteries with limited capacities, and it is often  costly  or  simply  impossible  to  replace  and/or  recharge  batteries, especially in remote and hostile environments. Obviously, to achieve a long life of the  network it is important  to conserve battery  power. Therefore, lifetime optimization is one of the most critical issues in wireless sensor networks. On the other hand we must guarantee  coverage over the area of interest. To fulfill these two objectives, the main idea  is to take advantage of overlapping sensing regions to turn-off redundant sensor nodes  and thus save energy. In this paper, we concentrate  on the area coverage  problem, with the  objective of maximizing the network lifetime by using an optimized multiround scheduling.
+We study the problem of designing an energy-efficient optimization algorithm that divides the sensor nodes in a WSN into multiple cover sets such that the area of interest is monitored as long as possible. Providing multiple cover sets can be used to improve the energy efficiency of WSNs. Therefore, in order to increase the longevity of the WSN and conserve the energy, it can be useful to provide multiple cover sets in one time and schedule them for multiple rounds, so that the battery life of a sensor is not wasted due to the repeated execution of the coverage optimization algorithm, as well as the information exchange and leader election.
 
 The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization protocol) presented in this chapter is an extension of the approach introduced in chapter 4. Simulation results have shown that it was more interesting to divide the area into several subregions, given the computation complexity. Compared to our protocol in chapter 4, in this one we study the possibility of dividing the sensing phase into multiple rounds. In fact, in this chapter we make a multiround optimization while it was a single round optimization in our protocol in chapter 4.
 
@@ -47,7 +29,7 @@ results. The chapter ends with a conclusion and some suggestions for further wor
 \section{MuDiLCO Protocol Description}
 \label{ch5:sec:02}
 \noindent In this section, we introduce the MuDiLCO protocol which is distributed on each subregion in the area of interest. It is based on two energy-efficient
-mechanisms: subdividing the area of interest into several subregions (like cluster architecture) using divide and conquer method, where the sensor nodes cooperate within each subregion as independent group in order to achieve a network leader election; and sensor activity scheduling for maintaining the coverage and prolonging the network lifetime, which are applied periodically. MuDiLCO protocol uses the same assumptions and network model that presented in chapter 4, section \ref{ch4:sec:02:01} and it has been used the primary point coverage model which is described in the same chapter, section \ref{ch4:sec:02:02}.
+mechanisms: subdividing the area of interest into several subregions (like cluster architecture) using divide and conquer method, where the sensor nodes cooperate within each subregion as independent group in order to achieve a network leader election; and sensor activity scheduling for maintaining the coverage and prolonging the network lifetime, which are applied periodically. MuDiLCO protocol uses the same assumptions and network model that presented in chapter 4, section \ref{ch4:sec:02:01} and it uses the primary point coverage model which is described in the same chapter, section \ref{ch4:sec:02:02}.
 
  
 \subsection{Background Idea and Algorithm}
@@ -60,7 +42,7 @@ As can be seen  in Figure~\ref{fig2},  our protocol  works in  periods fashion,
 where  each is  divided  into 4  phases: Information~Exchange,  Leader~Election,
 Decision, and Sensing. The information exchange among wireless sensor nodes is described in chapter 4, section \ref{ch4:sec:02:03:01}. The leader election in each subregion is explained in chapter 4, section \ref{ch4:sec:02:03:02}, but the difference in that the elected leader in each subregion is for each period. In decision phase, each WSNL will solve an integer  program to select which  cover sets  will be
 activated in  the following  sensing phase  to cover the  subregion to  which it belongs.  The integer  program will produce $T$ cover sets,  one for each round. The WSNL will send an Active-Sleep  packet to each sensor in the subregion based on the algorithm's results, indicating if the sensor should be active or not in
-each round  of the  sensing phase. Each sensing phase may be itself divided into $T$ rounds
+each round  of the  sensing phase. Each sensing phase is itself divided into $T$ rounds
 and for each round a set of sensors (a cover set) is responsible for the sensing
 task. Each sensor node in the subregion will
 receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
@@ -232,7 +214,7 @@ covered by at least  one sensor and, if it is not  always the case, overcoverage
 and undercoverage  variables help balancing the restriction  equations by taking
 positive values. The constraint  given by equation~(\ref{eq144}) guarantees that
 the sensor has enough energy ($RE_j$  corresponds to its remaining energy) to be
-alive during  the selected rounds knowing  that $E_{th}$ is the  amount of energy
+alive during  the selected rounds knowing  that $E_{th}$ is the amount of energy
 required to be alive during one round.
 
 There  are two main  objectives.  First,  we limit  the overcoverage  of primary
@@ -253,82 +235,26 @@ large compared to $W_{\theta}$.
 
 \subsection{Simulation Setup}
 \label{ch5:sec:04:01}
-We  conducted  a  series of  simulations  to  evaluate  the efficiency  and  the
+We conducted  a  series of  simulations  to  evaluate  the efficiency  and  the
 relevance  of our  approach,  using  the  discrete   event  simulator  OMNeT++
-\cite{ref158}. The simulation  parameters are summarized in Table~\ref{table3}.  Each experiment  for  a network  is  run over  25~different random topologies and  the results presented hereafter are  the average of these 25 runs.
-%Based on the results of our proposed work in~\cite{idrees2014coverage}, we found as the region of interest are divided into larger subregions as the network lifetime increased. In this simulation, the network are divided into 16 subregions. 
+\cite{ref158}. The simulation  parameters are summarized in chapter 4, Table~\ref{tablech4}.  Each experiment  for  a network  is  run over  25~different random topologies and  the results presented hereafter are  the average of these 25 runs.
 We  performed  simulations for  five  different  densities  varying from  50  to
 250~nodes deployed  over  a  $50 \times  25~m^2  $  sensing field.  More
 precisely, the  deployment is controlled  at a coarse  scale in order  to ensure
 that  the deployed  nodes can  cover the  sensing field  with the  given sensing
 range.
 
-%%RC these parameters are realistic?
-%% maybe we can increase the field and sensing range. 5mfor Rs it seems very small... what do the other good papers consider ?
-
-\begin{table}[ht]
-\caption{Relevant parameters for network initializing.}
-% title of Table
-\centering
-% used for centering table
-\begin{tabular}{c|c}
-% centered columns (4 columns)
-      \hline
-%inserts double horizontal lines
-Parameter & Value  \\ [0.5ex]
-   
-%Case & Strategy (with Two Leaders) & Strategy (with One Leader) & Simple Heuristic \\ [0.5ex]
-% inserts table
-%heading
-\hline
-% inserts single horizontal line
-Sensing field size & $(50 \times 25)~m^2 $   \\
-% inserting body of the table
-%\hline
-Network size &  50, 100, 150, 200 and 250~nodes   \\
-%\hline
-Initial energy  & 500-700~joules  \\  
-%\hline
-Sensing time for one round & 60 Minutes \\
-$E_{th}$ & 36 Joules\\
-$R_s$ & 5~m   \\     
-%\hline
-$W_{\Theta}$ & 1   \\
-% [1ex] adds vertical space
-%\hline
-$W_{U}$ & $|P|^2$
-%inserts single line
-\end{tabular}
-\label{table3}
-% is used to refer this table in the text
-\end{table}
-  
-Our protocol  is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5, and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of rounds in one sensing period).  In  the following, we will make comparisons with two other methods. The first method, called DESK and proposed by \cite{DESK}, is  a   fully  distributed  coverage   algorithm.   The  second   method is called
-GAF~\cite{GAF}, consists in dividing  the region into fixed squares.
-During the decision  phase, in each square, one sensor is  then chosen to remain active during the sensing phase time.
-
-Some preliminary experiments were performed in chapter 4 to study the choice of the number of subregions  which subdivides  the  sensing field,  considering different  network
-sizes. They show that as the number of subregions increases, so does the network
-lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random
-network  disconnection due  to node  failures.  However,  too  many subdivisions
-reduce the advantage  of the optimization. In fact, there  is a balance between
-the  benefit  from the  optimization  and the  execution  time  needed to  solve
-it. Therefore, we have set the number of subregions to 16 rather than 32.
-
-We used the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, we employed an energy consumption model, which is presented in chapter 4, section \ref{ch4:sec:04:03}. 
-
-%The initial energy of each node  is randomly set in the interval $[500;700]$.  A sensor node  will not participate in the  next round if its  remaining energy is less than  $E_{th}=36~\mbox{Joules}$, the minimum  energy needed for the  node to stay alive  during one round.  This value has  been computed by  multiplying the energy consumed in  active state (9.72 mW) by the time in second  for one round (3600 seconds). According to the  interval of initial energy, a sensor may be alive during at most 20 rounds.
+Our protocol  is declined into four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5, and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of rounds in one sensing period).  In  the following, we will make comparisons with two other methods. DESK \cite{DESK} and GAF~\cite{GAF}.
+%Some preliminary experiments were performed in chapter 4 to study the choice of the number of subregions  which subdivides  the  sensing field,  considering different  network sizes. They show that as the number of subregions increases, so does the network lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random network  disconnection due  to node  failures.  However,  too  many subdivisions reduce the advantage  of the optimization. In fact, there  is a balance between the  benefit  from the  optimization  and the  execution  time  needed to  solve it. Therefore, 
+we set the number of subregions to 16 rather than 32 as explained in chapter 4, section ref{ch4:sec:04:05}. We use the modeling language and the optimization solver which are mentioned in chapter 4, section \ref{ch4:sec:04:02}. In addition, the energy consumption model is presented in chapter 4, section \ref{ch4:sec:04:03}. 
 
 \subsection{Metrics}
 \label{ch5:sec:04:02}
 To evaluate our approach we consider the following performance metrics:
 
-\begin{enumerate}[i]
+\begin{enumerate}[i)]
   
-\item {{\bf Coverage Ratio (CR)}:} the coverage ratio measures how much of the area
-  of a sensor field is covered. In our case, the sensing field is represented as
-  a connected grid  of points and we use  each grid point as a  sample point to
-  compute the coverage. The coverage ratio can be calculated by:
+\item {{\bf Coverage Ratio (CR)}:} The coverage ratio can be calculated by:
 \begin{equation*}
 \scriptsize
 \mbox{CR}(\%) = \frac{\mbox{$n^t$}}{\mbox{$N$}} \times 100,
@@ -338,19 +264,17 @@ subregions during round $t$ in the current sensing phase and $N$ is the total nu
 of grid points  in the sensing field of  the network. In our simulations $N = 51
 \times 26 = 1326$ grid points.
 
-\item{{\bf Number  of Active Sensors Ratio  (ASR)}:} it is important  to have as
-  few  active  nodes  as  possible  in  each  round, in  order  to  minimize  the
-  communication overhead  and maximize the network lifetime.  The Active Sensors
-  Ratio is defined as follows:
+\item{{\bf Number  of Active Sensors Ratio  (ASR)}:}  The Active Sensors
+  Ratio for round t is defined as follows:
 \begin{equation*}
-\scriptsize  \mbox{ASR}(\%) = \frac{\sum\limits_{r=1}^R
+\scriptsize  \mbox{$ASR^t$}(\%) = \frac{\sum\limits_{r=1}^R
   \mbox{$A_r^t$}}{\mbox{$|J|$}} \times 100,
 \end{equation*}
 where $A_r^t$ is the number of  active sensors in the subregion $r$ during round
 $t$ in the  current sensing phase, $|J|$  is the total number of  sensors in the
 network, and $R$ is the total number of subregions in the network.
 
-\item {{\bf Network Lifetime}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+\item {{\bf Network Lifetime}:} Described in chapter 4, section \ref{ch4:sec:04:04}.
 
 \item {{\bf  Energy Consumption  (EC)}:} the average energy consumption  can be
   seen as the total energy consumed by the sensors during the $Lifetime_{95}$ or
@@ -360,11 +284,11 @@ network, and $R$ is the total number of subregions in the network.
  % New version with global loops on period
   \begin{equation*}
     \scriptsize
-    \mbox{EC} = \frac{\sum\limits_{m=1}^{M_L} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T_m} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M_L} T_m},
+    \mbox{EC} = \frac{\sum\limits_{m=1}^{M} \left[ \left( E^{\mbox{com}}_m+E^{\mbox{list}}_m+E^{\mbox{comp}}_m \right) +\sum\limits_{t=1}^{T} \left( E^{a}_t+E^{s}_t \right) \right]}{\sum\limits_{m=1}^{M} T},
   \end{equation*}
 
 
-where  $M_L$ is  the number  of periods  and  $T_m$ the  number of rounds in  a
+where  $M$ is  the number  of periods  and  $T$ the  number of rounds in  a
 period~$m$, both  during $Lifetime_{95}$  or $Lifetime_{50}$. The total energy
 consumed by the  sensors (EC) comes through taking  into consideration four main
 energy  factors.   The  first  one  ,  denoted  $E^{\scriptsize  \mbox{com}}_m$,
@@ -377,9 +301,9 @@ nodes to solve the integer program during a period. Finally, $E^a_t$ and $E^s_t$
 indicate the energy consumed by the whole network in round $t$.
 
 
-\item {{\bf Execution Time}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+\item {{\bf Execution Time}:} Described in chapter 4, section \ref{ch4:sec:04:04}.
   
-\item {{\bf Stopped simulation runs}:} is described in chapter 4, section \ref{ch4:sec:04:04}.
+\item {{\bf Stopped simulation runs}:} Described in chapter 4, section \ref{ch4:sec:04:04}.
 
 \end{enumerate}
 
@@ -389,7 +313,7 @@ indicate the energy consumed by the whole network in round $t$.
 \label{ch5:sec:04:02}
 
 
-\begin{enumerate}[(i)]
+\begin{enumerate}[i)]
 
 \item {{\bf Coverage Ratio}}
 %\subsection{Coverage ratio} 
@@ -400,7 +324,7 @@ can notice that for the first thirty rounds both DESK and GAF provide a coverage
 which is a little bit better than the one of MuDiLCO.  
 
 This is due  to the fact that, in comparison with  MuDiLCO which uses optimization
-to put in  SLEEP status redundant sensors, more sensor  nodes remain active with
+to put in  sleep status redundant sensors, more sensor  nodes remain active with
 DESK and GAF. As a consequence, when the number of  rounds increases, a larger
 number of node failures  can be observed in DESK and GAF,  resulting in a faster
 decrease of the coverage ratio.   Furthermore, our protocol allows to maintain a
@@ -410,7 +334,7 @@ coverage ratios of the  area of interest for a larger number  of rounds. It also
 means that MuDiLCO saves more energy,  with fewer dead nodes, at most for several
 rounds, and thus should extend the network lifetime.
 
-\begin{figure}[ht!]
+\begin{figure}[h!]
 \centering
  \includegraphics[scale=0.8] {Figures/ch5/R1/CR.pdf}   
 \caption{Average coverage ratio for 150 deployed nodes}
@@ -426,13 +350,13 @@ It is crucial to have as few active nodes as possible in each round, in order to
 minimize    the    communication    overhead    and   maximize    the    network
 lifetime. Figure~\ref{fig4}  presents the active  sensor ratio for  150 deployed
 nodes all along the network lifetime. It appears that up to round thirteen, DESK
-and GAF have  respectively 37.6\% and 44.8\% of nodes  in ACTIVE status, whereas
+and GAF have  respectively 37.6\% and 44.8\% of nodes  in active mode, whereas
 MuDiLCO clearly  outperforms them  with only 24.8\%  of active nodes.  After the
 thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
 with  the  dual  observation  of  higher  level  of  coverage  made  previously.
 Obviously, in  that case, DESK and GAF have fewer active nodes since they have activated many nodes  in the beginning. Anyway, MuDiLCO  activates the available nodes in a more efficient manner.
 
-\begin{figure}[ht!]
+\begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch5/R1/ASR.pdf}  
 \caption{Active sensors ratio for 150 deployed nodes}
@@ -453,7 +377,7 @@ emphasize that the  simulation continues as long as a network  in a subregion is
 still connected.
 
 
-\begin{figure}[ht!]
+\begin{figure}[h!]
 \centering
 \includegraphics[scale=0.8]{Figures/ch5/R1/SR.pdf} 
 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
@@ -488,7 +412,7 @@ network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
 
 
 The  results  show  that  MuDiLCO  is  the  most  competitive  from  the  energy consumption point of view.  The  other approaches have a high energy consumption due  to activating a  larger number  of redundant  nodes, as  well as  the energy consumed during  the different  status of the  sensor node. Among  the different versions of our protocol, the MuDiLCO-7  one consumes more energy than the other versions. This is  easy to understand since the bigger the  number of rounds and
-the number of  sensors involved in the integer program is  the larger the time computation to solve the optimization problem is. To improve the performances of MuDiLCO-7, we  should increase the  number of subregions  in order to  have fewer sensors to consider in the integer program.
+the number of  sensors involved in the integer program is, the larger the time computation to solve the optimization problem is. To improve the performances of MuDiLCO-7, we  should increase the  number of subregions  in order to  have fewer sensors to consider in the integer program.
 
 
 
@@ -502,7 +426,7 @@ seconds (needed to solve optimization problem) for different values of $T$. The
 
 %The original execution time  is computed on a laptop  DELL with Intel Core~i3~2370~M (2.4 GHz)  processor (2  cores) and the  MIPS (Million Instructions  Per Second) rate equal to 35330. To be consistent  with the use of a sensor node with Atmels AVR ATmega103L  microcontroller (6 MHz) and  a MIPS rate  equal to 6 to  run the optimization   resolution,   this  time   is   multiplied   by  2944.2   $\left( \frac{35330}{2} \times  \frac{1}{6} \right)$ and  reported on Figure~\ref{fig77} for different network sizes.
 
-\begin{figure}[ht!]
+\begin{figure}[H]
 \centering
 \includegraphics[scale=0.8]{Figures/ch5/R1/T.pdf}  
 \caption{Execution Time (in seconds)}
@@ -510,7 +434,7 @@ seconds (needed to solve optimization problem) for different values of $T$. The
 \end{figure} 
 
 As expected,  the execution time increases  with the number of  rounds $T$ taken into account to schedule the sensing phase. The times obtained for $T=1,3$ or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor node, especially when  the sensor network size increases.   Again, we can notice that if we want  to schedule the nodes activities for a  large number of rounds,
-we need to choose a relevant number of subregions in order to avoid a complicated and cumbersome optimization.  On the one hand, a large value  for $T$ permits to reduce the  energy overhead due  to the three  pre-sensing phases, on  the other hand  a leader  node may  waste a  considerable amount  of energy  to  solve the optimization problem.
+we need to choose a relevant number of subregions in order to avoid a complicated and cumbersome optimization.  On the one hand, a large value  for $T$ permits to reduce the  energy overhead due  to the three  pre-sensing phases, on  the other hand  a leader  node may  waste a  considerable amount  of energy  to  solve the optimization problem. \\
 
 
 
@@ -524,7 +448,7 @@ This  point was  already noticed  in \ref{subsec:EC} devoted  to the
 energy consumption,  since network lifetime and energy  consumption are directly linked.
 
 
-\begin{figure}[h!]
+\begin{figure}[hi]
 \centering
 % \begin{multicols}{0}
 \centering
@@ -550,7 +474,7 @@ called MuDiLCO (Multiround  Distributed Lifetime Coverage Optimization) combines
 
 The activity  scheduling in each subregion  works in periods,  where each period consists of four  phases: (i) Information Exchange, (ii)  Leader Election, (iii) Decision Phase to plan the activity  of the sensors over $T$ rounds, (iv) Sensing Phase itself divided into T rounds.
 
-Simulations  results show the  relevance of  the proposed  protocol in  terms of lifetime, coverage  ratio, active  sensors ratio, energy  consumption, execution time. Indeed,  when dealing with  large wireless sensor networks,  a distributed approach, like  the one we  propose, allows to  reduce the difficulty of  a single global optimization problem by partitioning it into many smaller problems, one per subregion, that can be solved  more easily. Nevertheless, results also show that it is not possible to plan the activity of sensors over too many rounds because the resulting optimization problem leads to too high-resolution times and thus to an excessive energy consumption.
+Simulations  results show the  relevance of  the proposed  protocol in  terms of lifetime, coverage  ratio, active  sensors ratio, energy  consumption, execution time. Indeed,  when dealing with  large wireless sensor networks,  a distributed approach, like  the one we  propose, allows to  reduce the difficulty of  a single global optimization problem by partitioning it into many smaller problems, one per subregion, that can be solved  more easily. Nevertheless, results also show that it is not possible to plan the activity of sensors over too many rounds because the resulting optimization problem leads to too high-resolution times and thus to an excessive energy consumption. 
 
 
 
